ece 2070 lecture 1
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1 ECE 2070 Basic Electrical Engineering
ECE 307 Lecture 1
DC Circuit Components, Connections, and KCL
Department of Electrical and Computer
Engineering
Clemson University
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2 ECE 2070 Basic Electrical Engineering
Electric Charge
Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. The SI unit of charge is Coulomb.
Electric charges are quantized It comes in integer multiples of individual small units called the
elementary charge (e), approximately equal to 1.6021019 coulombs (except for particles called quarks, which have charges that are integer multiples of e/3).
There are two types of charges: positive and negative. The proton has a charge of +e, and the electron has a charge of e.
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Electrical Work
Electrical work is the work done on a charged particle by an electric field. The SI unit for electric work is Joule.
Q is the charge of the particle, E is the electric field
F = q0E
a
b
+++++++++++++
- - - - - - - - - - - - -
Q
Q
F = q0E
ha
hb
a
b F = mg
F = mg
( )ab a bW mg h h
b
ab
a
W Q E dr
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4 ECE 2070 Basic Electrical Engineering
Electric Potential
The electric potential at a point in an electric field is defined as the work done in moving a unit positive
charge from infinity to that point.
The SI unit for electrical potential is Volt.
The electric potential difference
b
abab a b
a
WV V V
Q E dr
a
aa
WV
Q
E dr
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5 ECE 2070 Basic Electrical Engineering
Electric Current
Electric Current is defined as the time flow rate of electric charges
The SI unit for electric current is Ampere [coulombs per second)
The Electrical Engineering convention
The positive direction of current flow is that of positive charges.
Direct Current (DC): the flow of electric charges (current) is unidirectional.
Alternating Current (AC): the flow of electric charges (current) periodically reverses its direction.
dQI
dt
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Electric Power
Electric power, like mechanical power, is the rate of doing work, measured in watts [joules per second].
Electrical Engineering convention
The power dissipated by a load is a positive quantity
Power is generated/stored (negative) or dissipated (positive) when charges are moved between different
electric potentials.
Work Work Charge = =
Time Charge TimeElectric Power Voltage Current
P VI
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Electric Circuit Performs a function: oProcess Information
oTransfer Power
Characterized by: oVoltages
oCurrents
oPower
oEnergy
Circuit Components
Resistor Voltage Source Current Source Switch
Connections
Terminal Node Branch Loop Mesh
Similar
Electric Circuit
Reductions
Source Transformation Parallel Series Thevenin Equivalent Norton Equivalent
Analysis Tools
Kirchoffs Current Law
Node Voltage Method Kirchoffs Voltage Law
Mesh Current Method Superposition
Overview of DC Electric Circuits
DC Lecture 1 -
DC Circuit Components,
Connections, and KCL
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Overview of Lecture
Introduce Six Elements Used in a DC Circuit
Constant Voltage Source
Constant Current Source
Resistor
Open Circuit, Short Circuit, Switch
Connect the Elements to Build a Circuit
Define Connection Terminology: Terminal, Node, Branch, Loop, Mesh
Define Series and Parallel Connections
Kirchhoffs Current Law (KCL)
Describes the currents at a connection
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Constant Voltage Source
Examples of Constant Voltage Sources:
Car Battery supplies
constant 12V to power the
lights and accessories
AA Battery used in a
flashlight to supply a
constant 1.5V.
Solar Cell used to convert
light into electricity to power
this toy robot creates 0.5V
constant voltage.
Rechargeable Battery
supplies 3.7V to power
the cell phone
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Mathematical Model:
Voltage is Constant Current oCurrent is determined by
connections to other
components
oCan supply any current
Symbol:
Svor
Time Volt
age
Constant -> no change over time
Behavior:
Produces a constant voltage that
is not affected by connections to
other components
+ -
+
- Sv
Constant Voltage Source
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What does it do when connected to other components?
Constant Voltage Source
Sv+ -
Electric
Circuit
Case 2:
The electric circuit does work to
charge the battery
-
Sv+ -
Battery
Charging
Circuit
-
Current results from this connection Current results from this connection
Case 1:
Does work to move electrons and
supply energy to the rest of the
electric circuit
Note: We will have to solve the entire circuit in order
to know the amount of current.
i i
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Constant Current Source
Examples of Constant Current Sources:
Welder supplies constant
current to create the heat
needed to fuse metal pieces.
Cell Phone charger
supplies constant current at
the beginning of a full-
charge cycle.
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Constant Current Source
si
Time Curr
ent Constant -> no change over time
Behavior:
Produces a constant current that
is not affected by connections to
other components
Mathematical Model:
Current is Constant Voltage oVoltage is determined by
connections to other
components
oCan supply any voltage
Symbol:
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Constant Current Source
si
What does it do when connected to other components?
Does work to move electrons and supply energy to the rest of the electric
circuit
Electric
Circuit
-
A voltage can be
measured across
the current
source as a result
of this
connection
+
-
v
Note: We will have to solve the entire circuit in
order to know the amount of voltage.
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Resistor
Examples of Resistors:
The Heating Element of a
toaster (the part that gets hot)
resists the flow of electrons and
gets hot.
The Filament in a light bulb
(the part that produces light)
resists the flow of electrons and
gets very hot to produce light.
An extension cord is used
to connect appliances and
has very low resistance.
The resistance of the extension cord is not zero and can be
significant depending on the application.
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Resistor
R
Voltage
Cu
rren
t
1slope =
is constant.R
Behavior:
Constant relationship between
voltage and current.
Mathematical Model:
Constant R summarizes material properties, temperature, and size.
Ohms Law relates the voltage and current using R:
v = iR
Symbol:
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Resistor
R
What does it do when connected to other components?
Resists the flow of electrons. A resistor removes energy from the circuit
and dissipates it as heat.
Electric
Circuit
A voltage can be
measured across
the resistor as a
result of this
connection
+
-
v
Current results from this connection
-
Note: We will have to solve the entire circuit in order to
know either the voltage or the current. We do know that
voltage and current are related by Ohms Law as v = iR
i
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Application of Ohms Law
Rv
R is a circuit model of a physical material that
has length, width, height, and property of
conductivity that constitute the resistance.
Examples (given same size):
Copper wire (low resistance)
Nichrome wire (medium resistance)
Gold wire (low resistance)
Insulation on wire (high resistance)
For the current referenced into a voltage drop as shown
v=iR
+
-
i
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Application of Ohms Law
Must adjust the sign (+/-) in Ohms law for other referenced directions,
This is the standard
convention
v= - iR
v= iR
Rv
+
-
Rv
+
-
i i
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Example 1: Applying Ohms Law given fixed voltage
and current references
v= - iR
= -(-2A)(10W)
= 20V
v= iR
= 2A(10W)
= 20V
v= iR
= (-2A)(10W)
= -20V
These are all the same circuit. 2A goes into the resistor from the top and there is a
20 V drop from top to bottom.
10W
2A
v
+
-
10W
2A
v
+
-
10W
2A
v
+
-
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Open and Short Circuits
Resistance is Electric
Circuit
NO current can be
measured across
the opening
+
-
v
No Current
-
Short Circuit:
No resistance to current flow, ~ zero R
Open Circuit:
No current can flow, ~ infinite R
Electric
Circuit
NO voltage can be
measured across
the short
+
-
v
Current
-
Resistance is zero
i i
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Switch
Examples of Switches:
Switch on the wall turns
the lights on or off. Each button on the phone
or key on the keyboard is a
Switch.
Switch on the coffee
maker turns the appliance
on or off.
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Switch
Behavior:
Can stop or allow the flow of current.
Mathematical Model:
No current flows when the switch is open.
Current flows freely when switch is closed.
Symbol:
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Switch
What does it do when connected to other components?
Connects or disconnects part of the circuit
RElectric
Circuit
NO current can be
measured across
the opening
+
-
v
No Current
-
Closed:
Acts like a short circuit
Open:
Acts like an open circuit
RElectric
Circuit
NO voltage can be
measured across
the switch
+
-
v=0V
Current
-
i i
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Connect Components to Create an Electric Circuit
Example: Connect a battery and a resistor to build a portable light.
Device: Flashlight
1.5V 1W 1.5V
Circuit Model
1.5A
1.5A
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Electric Circuit (Electric Network)
Connection of Components
Terms to describe the connection of components
Terminal
Node
Branch
Loop
Mesh
Learning a new
vocabulary !
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Electric Circuit Connections
Terminal point where a component or part of the circuit connects to other components or other parts of
the circuit
Node connection point
Electrically anywhere
in here is the
connection point
Pick a point and call it the node
R3
R1
R2
R3
R1
R4
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Terminals v1 + - R
v1 + -
R1
R2
R3 Each element alone
has two terminals
A connection of
components has terminals
v1 + -
R1
R2
R3
R4
These internal
connections are
not the terminals
of the connected
components.
Example 2: Identify Terminals
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Example 3: Identify Nodes
Electrically,
anywhere along
the wires in this
area is the
connection point
Pick a point and
call it the node
Note that this connection
is an electrical circuit and
could be a model for a
system such as the
electrical system in a car
R1 + - R2 R3 v1
Label the nodes in the circuit.
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Electric Circuit Connections
Branch portion of a circuit with only two external
terminals
terminals
Each element is a branch.
The connection between
and is also a branch 1t 3t
Each element is a branch. The
connection is NOT a branch
because it has 3 external terminals
t1 , t3, and t4 and three
components connect at t2 .
R1
v1 + -
3t
2t
1t
R1
R2
v1 + -
4t
1t
2t
3t
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3W
Example 4: Identify Branches
Find branches in the circuit.
28A
2W
4W6W
1W 2W
+ -
40V
Each of the components are individually a branch, 8 components means 8 branches.
First identify the nodes.
There is a branch containing the 40V source and the 3W and 1W resistors the connection has two terminals.
The branch at the right has two terminals that connect this sub-circuit to the rest of the circuit.
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Parallel Connection
Elements of a circuit which share the same two nodes
+ - R1 R3 R2 i1
Electrically,
anywhere along
the wires in this
area is the
connection point
Pick a point and
call it the node
v1
All components of the circuit connect to the same two
nodes and are therefore in parallel.
We often use the symbol || to indicate that elements are in parallel, here v1 || i1 || R1 || R2 || R3
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28A
2W3W
4W6W
1W 2W
+ -
Example 5: Indentify Parallel Elements
40V
4 W and 28A source are
in parallel. The branch containing
the 40V source and the
3W and 1W resistors is
in parallel with 6W
resistor
Which elements in the circuit are connected in parallel?
First indentify the nodes.
No other individual
components are in parallel
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R1
R2 R3
v1 + - R5 R4
Electric Circuit Connections
Loop a closed connection of branches
Mesh a loop that does not contain other loops
How many nodes?
How many meshes?
How many loops?
5
2
The two meshes plus the
third exterior loop
2+1=3
Form a closed connection of branches by starting at a node and
traversing the circuit until we get back to the starting node.
Cannot use the same node twice.
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+ -
R1
+ -
R2
R3 R4 v2 i1 v1
1N 3N2N
4N
Example 6: Identify nodes, loops, meshes
How many nodes?
How many meshes?
How many loops?
What is not a loop?
5
4
5 + +
A path that crosses the same node twice
R5
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Kirchhoffs Current Law (KCL)
Equal amounts of charge enter and exit a node.
Algebraic sum of currents into and out of a node is zero:
Convention 1: Current labeled as pointing into a node is given a negative sign in the summation and current labeled as pointing out of the node is positive.
Convention 2: Current labeled as pointing into a node is given a positive sign in the summation and current labeled as pointing out of the node is negative.
1
0N
n
i
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Example 7: Applying KCL
1i2i
3i
4i
Find i3 in terms of the other currents.
4
1 2 3 4
1(i out of node +)
0 0n
i i i i i
3 1 2 4i i i i
Node
Using Convention 1:
4
1 2 3 4
1(i out of node -)
0 0n
i i i i i
3 1 2 4i i i i
Using Convention 2: Both conventions yield the
same result. We will
generally use Convention 1
Solve for i3:
Solve for i3:
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Example 7 (cont): Applying KCL
1i2i
3i
4i
Given:
1 5Ai
2 3Ai
4 2Ai
Find : 3i4
1 2 3 4
1(i out of node +)
0 0n
i i i i i
3 1 2 4 ( 5 ) 3 ( 2 )
0A
i i i i A A A
Note: i2 = -3A means
that the current actually
flows in the direction
opposite to the arrow
Node
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39 ECE 2070 Basic Electrical Engineering
Example 8: Applying KCL
1i
2i
3i
4i
Same problem with some of the current directions
changed. Find i3 in terms of the other currents.
4
1 2 3 4
1(i out of node +)
0 0n
i i i i i
3 1 2 4i i i i
Node
Using Convention 1:
4
1 2 3 4
1(i out of node -)
0 0n
i i i i i
3 1 2 4i i i i
Using Convention 2: Both conventions yield the
same result. We will
generally use Convention 1
Solve for i3:
Solve for i3:
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R1 + - R2 R3
R4
v1
Example 9: Applying KCL in a Circuit
1N
2N
KCL at Node 1 :
at Node 2:
5
1 2 3 4
1(i out of node +)
0 0Sn
i i i i i i
5
1 2 3 4
1(i out of node +)
0 0Sn
i i i i i i
i1 i2 i3
i4
is
Apply KCL at each node.
Identify the nodes in the circuit and label.
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Example 9 (cont): Applying KCL in a Circuit
1 2 35A 1ASi , i i i
Node 1:
2:
4 45A 1A 1A 1A 0 2Ai i
4 45A 1A 1A 1A 0 2Ai i
If we knew some actual values:
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Example 10: Solving a Circuit Using KCL
What is the current through the 5W resistor?
4
1(i out of node 1)
0 -5 -15 8 0an
i A A A i
5 15 -8 12ai A A A A
12 5 60Va av i R A W Once we know the current in a resistor, we can use Ohms law to find the voltage:
KCL at the
top node
yields:
ia 15A 8A 5A 5W
Identify the nodes in the circuit and apply KCL to create equations to solve for ia.
We need to solve for ia.
+
-
va
Here we only
needed to write 1
equation and solve
for the 1 unknown.
1
2
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Series Connections
Elements of a circuit connected so that the current out
of one component goes into the next.
3W
28A
2W
4W6W
1W 2W
+ -
40V
We say that the 40V source, the 3W resistor, and the 1W
resistor are connected in series.
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Example 11: Show that series components have the
same current.
a b ci i i
3W
28A
2W
4W6W
1W 2W
+ -
40V
ia
ib
ic
N1 N2 N3
N4 N5 N6
Write KCL equations at nodes N1 and N4:
4
1
1(i out of node +)
: 0 0a bn
N i i i
4
2
1(i out of node +)
: 0 0b cn
N i i i
4
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Electric Circuit Performs a function: oProcess Information
oTransfer Power
Characterized by: oVoltages
oCurrents
oPower
oEnergy
Circuit Components
Resistor Voltage Source Current Source Switch
Connections
Terminal Node Branch Loop Mesh
Similar
Electric Circuit
Reductions
Source Transformation Parallel same voltage Series same current Thevenin Norton
Analysis Tools
Kirchoffs Current Law Node Voltage Method
Kirchoffs Voltage Law
Mesh Current Method Superposition
Summary
DC Lecture 1 -
DC Circuit Components,
Connections, and KCL
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